# INTEREST RATES

It is human nature to prefer immediate gratification. We dislike postponing consumption. If we are requested to delay our satisfaction, we demand a reward. This reward often takes the form of increased consumption at the later time. This same idea applies to money. Money, it has been observed, is only as good as what you can use it for. Whether dollars, rubles, or drachmas, money is a measure of the ability to consume. If we lend money we give up the possible immediate consumption it represents, and we expect a reward in the form of a greater return than the amount originally lent. In the case of money, the reward, or difference between what was lent and what is returned, is referred to as interest. Alternately, interest may be considered as rent.

A similar argument for interest is that the money could have been used to purchase assets. Those assets could then be rented to other parties (or used directly to produce a return). Interest, then, is compensation for rent or return foregone. More directly, interest is the cost of "renting" the money itself.

## MEASUREMENT

For reasons of comparability, interest is normally specified as a percentage rate of increase, rather than as an absolute amount. The "interest rate" is the percentage increase:

The interest rate is also sometimes described in terms of "basis points," with one basis point being one hundredth of 1 percent. The difference between the interest rate of 10.25 percent and the interest rate of 10.00 percent is 25 basis points.

The specification of the interest rate is not complete unless the period over which the increase occurs is specified. Although interest rates are stated in terms of an annual rate, interest may be computed and become due more often than annually. The period over which interest is calculated is called the compounding period. The standard period for compounding is one year, but other intervals such as quarterly, daily, or even continuous compounding are not unusual.

Where the compounding period is shorter than one year, the per period rate must be converted to an annual rate. The simplest method of annualizing is called "simple interest" or annual percentage rate (APR), which is computed by simply multiplying the per period rate by the number of periods in a year. The "yield" or interest rate on bonds, for instance, is normally computed on a semiannual basis and then converted to an annual rate by multiplying by two. Although this rate is incorrect when the compounding period is less than one year, it has become convention, a holdover from days of hand calculation. The realized or "effective" annual interest rate will be higher than the stated annual rate due to the interest on interest effect. For example, suppose that \$100 is borrowed at 10 percent compounded semiannually. At the end of six months, \$50 is paid. The reduces the amount in the hands of the borrower over the next six months to \$95.00. The borrower thus pays \$10.00 annual interest to borrow an average of \$97.50—an actual rate of about 10.25 percent. Alternately, if \$100.00 is invested for one year at 6 percent compounded annually, the lender will receive \$106.00 at the end of the year, a return of 6 percent to the lender. The same \$100.00 invested at 6 percent compounded semiannually would lead to interest payments of \$3.00 at six months and at one year. The \$3.00 payment received at six months would be added to the principal amount and reinvested at 6 percent, however, so that the interest payment over the second six months would be \$3.30. Under semiannual compounding, the investor's account at the end of the year would have the original investment of \$100.00, the six-month interest payment of \$3.00, and the one-year interest payment of \$3.30—a total of \$106.30. This would be an actual or realized rate of return of 6.3 percent. The extra \$0.30 is interest on the interest. The effect of interest on interest and compounding more often than once a period is not large for any one period, but over long periods the realized amount can be significantly different. If the above \$100.00 had been invested at 6 percent for 20 years at simple interest—i.e., with no compounding, ignoring reinvestment of interest payments—the final amount would be the original \$100.00, plus 20 years' interest payments amounting to \$120.00, a total of \$220.00. If the interest payments are reinvested at 6 percent compounded annually, the final amount would be \$320.71, with interest on interest amounting to \$100.71. The same \$100 invested for 20 years at 6 percent compounded semiannually would increase to \$326.20. The \$5.49 increase over the amount earned under annual compounding would arise from interest on interest.

The interest rate computation that includes the compounding effect is called the annual percentage yield (APY), and is considered a superior measure of annualized interest rates. The APY is computed by compounding or multiplying the per period rates over the year to arrive at the effective annual rate:

Another misleading form of interest computation is "discounted in advance." In this form, the interest is deducted from the principal, and the borrower receives the net amount. This form can severely understate the interest rate. In our example, a one-year borrower would receive \$9.00, or \$10.00 principal less \$1.00 interest for one year, and would owe \$10.00 at the end of the year, effectively paying the interest at the time of borrowing. This is equivalent to paying \$1.00 to borrow \$9.00, a compound annual rate of 11.11 percent.

## DETERMINANTS OF INTEREST RATE LEVELS

The level of interest rates is set by supply and demand—i.e., when the amount of money supplied is equal to the amount that other economic units wish to borrow. The interesting question, however, is what factors influence supply and demand. Since interest is in the nature of a reward for postponing consumption, a higher interest rate can be expected to result in a greater supply of funds. Under different conditions, however, a given interest rate may result in a differing supply. Attitudes toward consumption are important, as shown by the differences between savings rates in different countries. Uncertainty about the economy may prompt more saving, as shown by the different attitudes of the "depression generation" and their children. Demand, on the other hand, depends on the investments available, and will be downward sweeping since more investments are profitable at lower interest rates. In periods of high growth or technological advancement, there will be more acceptable investment and greater demand. Future economic growth is affected by the rate of increase of population, the workforce, and the educational and skill level. Economic conditions and production possibilities set the general level of demand for funds.

The economic and other variables set the interest rate as a rate of increase in ability to consume. This rate of increase in ability to consume is called the "real" rate of interest. The "nominal" or dollar rate of interest measures the increase in dollars. Money is a measure of ability to consume, but the yardstick itself changes over time due to inflation. Inflation is a decrease in the purchasing power, or amount of consumption that can be acquired per monetary unit. Since it is the real rate of interest that controls the supply and demand of funds, the nominal interest rate must include a premium that compensates for any expected loss of purchasing power. The stated or nominal interest rate is then expressed as the real rate of interest plus an inflation premium:

where R N = the nominal rate of interest,
R R = the real rate of interest,
I = the expected rate of inflation.

For small rates of inflation the inflation rate itself is a good approximation of the premium required, and the last term is often ignored. For higher rates of inflation the last term becomes significant, and should be included. The higher level of interest rates in the early 1980s is partially due to the effects of actual or feared inflation.

Interest rates are also affected by and are an instrument of government policy. The Federal Reserve manages the amount of money in circulation, and affects the interest rates. Too rapid growth of the amount of money will have an immediate effect of decreasing interest rates, since supply is increased. Over the longer run, however, too rapid growth in the amount of money may result in inflation. Interest rates, reacting to the expectation of inflation, will increase. Too low a rate of growth in the amount of money, on the other hand, will result in a reduction of supply and higher interest rates. This in turn may hamper economic growth. If the economy stagnates, the eventual result may well be decreased interest rates.

Over time the Federal Reserve has placed varied emphasis on two policy targets. The first is the growth of the amount of money, while the second is interest rates. It would be incorrect to say that the Federal Reserve has "control" over either of these variables. This would be impossible in a dynamic economy such as that of the United States. Given the number of money-like arrangements, the definition of "money," much less its measurement, is difficult. The monetary tools of the Federal Reserve work most directly on short-term interest rates. Interest rates for longer maturities are indirectly affected through the market's perception of government policy and its economic effects. More recently, expectations of possible inflation have been a major concern to lenders and policy makers. Economic forces shape the level of interest rates, while governmental policies have some effect on economic forces. Foreign interest rates have become increasingly important. Major firms now routinely borrow in foreign markets, and lenders are increasingly willing to hold foreign debt. This forces some alignment of interest rates worldwide, and reduces the amount of control any nation has over its domestic conditions.

There are many forms of borrowing, and thus many interest rates. Borrowing and lending arrangements include personal loans, credit cards, mortgages, various federal and municipal government obligations, corporate bonds, and multiple other forms. Investors borrow when they trade on margin, firms borrow by using trade credit. The interest rate on different borrowing arrangements will be different, which is why the plural is used here. While economic and other variables set the general level of interest rates, specific interest rates are affected by other variables. While there are a multitude of factors affecting interest rates, they are generally grouped under differences in maturity, quality, and tax status.

## THE TERM STRUCTURE OF INTEREST RATES

Interest rates are also related to the maturity, or length of commitment, of the arrangement. The relationship is often described by a yield curve showing the interest rates for various maturities. There are several theories to explain this "term structure of interest rates." The first is called the "expectations theory." This theory holds that interest rates over longer periods are dependent on the series of short-term interest rates expected over that period—i.e., lenders are indifferent to the length of commitment, but require the same expected ending wealth regardless of whether they lend money once for ten years or they make a series of ten-year loans, each for one year. The motivation here is that if this relationship did not hold, investors would prefer the alternative with the higher ending wealth, forcing a readjustment of interest rates. Alternately, if the relationship did not hold, investors could arbitrage, selling the lower yielding alternative and investing the proceeds in the higher yielding alternative. This arbitrage would allow the arbitrager to make a return from a net zero investment. Under this theory, the yield curve would be upward sweeping if short-term interest rates were expected to increase in the future, and downward sweeping if short-term interest rates were expected to decrease in the future.

A second approach, called the "liquidity theory," suggests that investors are not indifferent as to the length of commitment. This argument suggests that lending for longer periods is more risky than short-term lending. The longer period makes prediction less accurate, and permits more opportunities for negative results. Investors prefer more liquid, shorter-term lending, and will not commit the funds for longer periods unless given a "liquidity premium" to compensate for this higher risk. Under only this approach, the yield curve would be upward sweeping at all times. Empirical observation of decreasing yield curves does not refute this theory, however, if it is combined with other theories. If the liquidity premium is superimposed on the expectation that short-term interest rates will decrease in the future, the result can be a yield curve that is still downward sweeping but less steep.

A third approach is called the "segmented markets" theory. As we have noted, interest rates depend on supply and demand. Segmented markets builds on this obvious statement, adding the idea that lenders and borrowers will have a "preferred habitat," or length of commitment. This preferred habitat comes about because of the desire of lenders and borrowers to reduce risk by matching the maturity of assets and liabilities. A lender with a liability that will come due in ten years, for example, avoids risk by lending with a maturity of ten years; a borrower whose use of the funds will pay off in ten years will borrow with a maturity of ten years. Borrowers and lenders are thus reluctant to leave their preferred maturity, and will not arbitrage. As a result, the interest rate for any given maturity will depend on the supply and demand for that given maturity.

In actuality, all of these theories are to some extent correct. Empirically, since World War 1I the yield curve has been predominantly upward sweeping, with long-term rates higher than short-term rates. Inverted, or downward sweeping yield curves in which long-term rates are lower than short-term rates, have been observed over shorter intervals. Long-term rates tend to have less volatility, and to move over a smaller range, than short-term rates.

## THE QUALITY STRUCTURE OF INTEREST RATES

The "quality" structure of interest rates describes the effect of uncertainty about receiving the specified reward. In the face of uncertainty about payments, lenders will demand a higher rate of return or "risk premium." The interest rate to a particular borrower will be the sum of a "risk-free" rate plus the risk premium. Default risk is not simply the failure to pay principal, but is rather a matter of degree. There are many possibilities short of complete loss, sometimes as small as a "skipped" or late payment. Loan arrangements with little probability of a problem are said to be of high quality.

The higher the severity and probability of a problem, or the lower the quality, the higher will be the risk premium. Treasury obligations, which are direct obligations of the U.S. government and assumed to have no default risk, are of the highest quality. Bonds issued by agencies of the government, which are not direct government obligations, are of only slightly lower quality since it is assumed the government would assume the responsibility. State and local bonds, called "municipals," vary widely in quality depending on the characteristics of the security and the issuer. The same variation is true of corporate bonds. These securities are sometimes "rated" as to quality by independent firms such as Standard & Poor's, Moody's, Duff & Phelps, and Fitch Investors Service. These ratings are widely used to classify bonds and are important factors in the interest rate, or "yield," provided to investors. Bonds below a certain rating are often referred to as junk bonds, and carry a higher interest rate.

This quality structure is also apparent in bank loan interest rates. The prime rate is the rate charged to large customers with established relationships. Borrowers with less admirable credit records (or smaller accounts that are comparatively more expensive) will pay a higher rate. Collateral is also important. Unsecured personal loans, such as credit card credit, will ordinarily pay a higher rate than car loans, which will in turn pay more than home mortgages. An important characteristic of loan arrangements is liquidity. An asset that can be converted to cash quickly at a fair price is liquid; if price concessions are required for rapid sale the asset is illiquid. Many loans have been relatively illiquid, so that once the loan is made the creditor was locked in. This lack of freedom of action increased the risk of the lender, resulting in higher interest rates. More recently, a number of classes of loans have been "securitized" by being bundled into portfolios against which securities are issued. This added liquidity reduces lender risk and lowers the interest rate on the underlying loan classes.

## TAX STATUS

The interest rate on bonds issued by state and local governments, called "municipal bonds," is lower than the interest rate on corporate bonds of the same quality. The reason for this difference is that the interest on these debt obligations is generally exempt from federal taxation. They are also often exempt from taxes of the state of issue. The real rate of increase in purchasing power from taxable federal and corporate debt instruments will be reduced by the taxes:

Since interest rates reflect the real rate or increase in purchasing power, taxable and nontaxable debt will have the same after-tax rate of return. This equilibrium will not hold for all investors because of differing tax rates. For investors with high tax rates, the after-tax rate of return on municipals may be higher, while for investors with low tax rates the return on corporate debt may be higher.

Another tax effect comes about because of the tax deductibility of some interest payments on personal taxes. The tax deductibility of interest on home mortgages effectively lowers the interest rate. This is reflected in the rapid increase in mortgage-based loans after interest on consumer debts was no longer tax deductible.

[ David E Upton ]